"America doesn't have friends," Henry Kissinger once observed, "America only has interests." By that logic, the Obama Administration may have been tempted, Friday, to cut President Hosni Mubarak loose  nothing personal, you understand, but the Egyptian president has become the focus of such intense hostility from his own people after 30 years of authoritarian rule that backing him in the face of a growing democratic rebellion could jeopardize long-term U.S. regional interests in Egypt.

As the streets of Cairo, Alexandria and Suez roiled with anti-regime protests on Friday, the Administration insisted that Mubarak's security forces refrain from using force against peaceful demonstrators, and instead not only respect their right to free speech and assembly, but also heed their grievances. The White House statements seemed increasingly to be addressed to the Egyptian "authorities" over Mubarak's head. Had President Obama actually spoken on the phone to this critically important U.S. ally amid the crisis that unfolded on Friday? No, he had not, conceded White House press secretary Robert Gibbs Friday afternoon, reiterating the mantras about restraint, reform and heeding protestors' demands. (See pictures of protests in Egypt.)

But the protestors' prime demand is precisely the one Mubarak has no intention of heeding: His own departure from power. As Dr. Mohammed ElBaradei, the moderate Nobel Peace Prize winning former nuclear inspector who has played a leading role in the emerging democracy movement made clear in an interview, Friday  before being placed under house arrest  "We are prepared to engage with the regime to ensure a smooth and orderly transition, but there is no question that Mubarak will have to leave."

When Mubarak failed to deliver a promised early evening national TV address, speculation grew that the regime had been rattled by the intensity of Friday's protests. And the fact that the army, sent onto the streets by Mubarak to enforce a curfew had shown up but appeared to adopt a relatively permissive attitude toward protestors fueled optimism that the strongman might be on the verge of fleeing. Suddenly, the name of Hussein Tantawi, the country's 75-year-old Defense Minister who had been in Washington on a previously scheduled visit during this week's protests, was being touted as a possible interim president. (See the ideology behind the Egyptian protests.)

Some analysts speculated that the U.S. may even have learned from President Ben Ali's collapse in Tunisia, and earlier failures such as the fall of the Shah of Iran in 1979, by engineering the departure of an autocrat whose rule had become untenable, in order to defuse the rebellion and have the transition to a more responsive government managed by a leadership that continued to prioritize U.S. regional interests. After all, the protestors had made clear they had no interest in promises of a kindler, gentler Mubarak, and would not rest until he was out of power. (See pictures of mansions ransacked in Tunisia.)

But Kissinger's rule applies as much to America's allies and proxies as it does to Washington: Mubarak's interests don't necessarily match America's. He's largely ignored years of pressure from the Obama Administration and its predecessors to introduce reforms aimed at avoiding the sort of scenario he now faces, and in a televised address finally delivered at midnight, local time, Mubarak came out swinging, firing his government and promising to name a new one on Saturday, proclaiming himself an agent of reform and human rights, and declaring that "We will continue our political, economic and social reforms for a free and democratic Egyptian society." In other words, he wasn't going anywhere. Indeed, Mubarak defended his crackdown, vowing that he would "protect" Egypt from the "anarchy" of the protesters.

The speech was widely derided on the streets, and analysts warned that it was likely to intensify protests. And lest anybody doubt that the White House recognized Mubarak's position as a statement of defiance toward Washington, President Obama announced an hour later that he'd spoken to his Egyptian counterpart after the speech, and had made "very clear" that Mubarak had an obligation to refrain from violence against peaceful protests, to turn the SMS and Internet platforms blocked by his regime back on, and to take "concrete steps" toward real reform. "Ultimately the future of Egypt will be determined by the Egyptian people," Obama said. "Governments have an obligation to respond to their citizens." Press Secretary Gibbs put a price tag on further Mubarak misbehavior, warning that the annual $1.3 billion aid package the U.S. sends to Egypt's security forces would be placed under review on the basis of Egypt's handling of the protests. (Read President Obama's remarks on Egypt.)

The Administration is caught in a bind, but it's more strategic than just moral: Supporting tyrants loathed by their own people but willing to do Washington's bidding in international matters is a decades-old U.S. tradition in the Middle East, as well as in Asia, Africa and Latin America. The problem with Mubarak is not simply that his methods are at odds with professed U.S. values; it's that his brittle autocracy appears to have entered a period of terminal decline, with the U.S. potentially on the wrong side of history. His ability to keep a lid on his citizenry may have been dealt a fatal blow by Friday's protests, in which tens of thousands lost their fear of challenging his power. For a day, ordinary Egyptians owned the streets, the security forces largely unable to restrain them  although the 26 dead by day's end underscored the bitterness of that struggle in some places. And as night fell on Cairo, the flames that consumed the headquarters of Mubarak's National Democratic Party served as an eloquent symbol of a spell broken. For a man on whose power such key U.S. interests as the Suez Canal trade routes and peace between Israel and its Arab neighbors depends, Mubarak is suddenly looking like not such a safe bet.

The logic of the long-term may dictate that the U.S. distance itself from Mubarak and ingratiate itself with a democratic opposition  most of which remains deeply skeptical of U.S. motives given its unconditional backing for the strongman until as recently as Tuesday, when Hillary Clinton's comments that the regime was "stable" and "looking for ways" to address protestors' grievances drew howls of protest. But the protest movement ranged against Mubarak is a broad church that includes elements that Washington views with suspicion, foremost among them the powerful Muslim Brotherhood. (See TIME's photo-essay "A Brief History of People Power.")

Whatever the optimal outcome for stability and U.S. interests, however, Mubarak has made clear he's staying put. That will mean intensified protest in the days and weeks to come. And the more bitter the struggle to remove him, the less likely are his long-term patrons to benefit strategically from the change.